Question: 6 people can paint 7 walls in 30 minutes. How many minutes will it take for 8 people to paint 8 walls? Round to the nearest minute.
We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 7\text{ walls}\\ p &= 6\text{ people}\\ t &= 30\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{7}{30 \cdot 6} = \dfrac{7}{180}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 8 walls with 8 people. $t = \dfrac{w}{r \cdot p} = \dfrac{8}{\dfrac{7}{180} \cdot 8} = \dfrac{8}{\dfrac{14}{45}} = \dfrac{180}{7}\text{ minutes}$ $= 25 \dfrac{5}{7}\text{ minutes}$ Round to the nearest minute: $t = 26\text{ minutes}$